title: A one-dimensional slope detection approach.
abstract: This paper extends the scale-invariant edge detector to the one-dimensional slope. It can accurately detect the slope and estimate its parameters. The method has been verified with several mathematical functions, sample sizes, and noise levels. A contrast-invariant operator is proposed to suppress noise. The inter-sample localization and interpolation greatly improve the accuracy. The proposed slope detector is also suitable for real-world signals. In additional to above-mentioned, a threshold formula is developed for the first derivative slope detector, and the upper-bound of the filterable noise level is also explored.
authors.affiliation: School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, 210094 China.
authors.forename: Xiaochun
authors.initials: X
authors.lastname: Zhang
authors.forename: Chuancai
authors.initials: C
authors.lastname: Liu
keywords: Error function; Gaussian; Interpolation; Localization; Noise suppression; Slope; Sub-sample; The first derivative operator; Threshold